<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.9.1"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Eigen: MathFunctionsImpl.h Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="resize.js"></script>
<script type="text/javascript" src="navtreedata.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
  $(document).ready(function() { init_search(); });
/* @license-end */
</script>
<script type="text/x-mathjax-config">
  MathJax.Hub.Config({
    extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
    jax: ["input/TeX","output/HTML-CSS"],
});
</script>
<script type="text/javascript" async="async" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js"></script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
<link href="eigendoxy.css" rel="stylesheet" type="text/css">
<!--  -->
<script type="text/javascript" src="eigen_navtree_hacks.js"></script>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
 <tbody>
 <tr style="height: 56px;">
  <td id="projectlogo"><img alt="Logo" src="Eigen_Silly_Professor_64x64.png"/></td>
  <td id="projectalign" style="padding-left: 0.5em;">
   <div id="projectname"><a href="http://eigen.tuxfamily.org">Eigen</a>
   &#160;<span id="projectnumber">3.4.90 (git rev 67eeba6e720c5745abc77ae6c92ce0a44aa7b7ae)</span>
   </div>
  </td>
   <td>        <div id="MSearchBox" class="MSearchBoxInactive">
        <span class="left">
          <img id="MSearchSelect" src="search/mag_sel.svg"
               onmouseover="return searchBox.OnSearchSelectShow()"
               onmouseout="return searchBox.OnSearchSelectHide()"
               alt=""/>
          <input type="text" id="MSearchField" value="Search" accesskey="S"
               onfocus="searchBox.OnSearchFieldFocus(true)" 
               onblur="searchBox.OnSearchFieldFocus(false)" 
               onkeyup="searchBox.OnSearchFieldChange(event)"/>
          </span><span class="right">
            <a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.svg" alt=""/></a>
          </span>
        </div>
</td>
 </tr>
 </tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.9.1 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
var searchBox = new SearchBox("searchBox", "search",false,'Search','.html');
/* @license-end */
</script>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
  <div id="nav-tree">
    <div id="nav-tree-contents">
      <div id="nav-sync" class="sync"></div>
    </div>
  </div>
  <div id="splitbar" style="-moz-user-select:none;" 
       class="ui-resizable-handle">
  </div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
$(document).ready(function(){initNavTree('MathFunctionsImpl_8h_source.html',''); initResizable(); });
/* @license-end */
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
     onmouseover="return searchBox.OnSearchSelectShow()"
     onmouseout="return searchBox.OnSearchSelectHide()"
     onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>

<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0" 
        name="MSearchResults" id="MSearchResults">
</iframe>
</div>

<div class="header">
  <div class="headertitle">
<div class="title">MathFunctionsImpl.h</div>  </div>
</div><!--header-->
<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2016 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; </div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#ifndef EIGEN_MATHFUNCTIONSIMPL_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#define EIGEN_MATHFUNCTIONSIMPL_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160; </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160; </div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Packet, <span class="keywordtype">int</span> Steps&gt;</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="keyword">struct </span>generic_reciprocal_newton_step {</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;  static_assert(Steps &gt; 0, <span class="stringliteral">&quot;Steps must be at least 1.&quot;</span>);</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE  Packet</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;  run(<span class="keyword">const</span> Packet&amp; a, <span class="keyword">const</span> Packet&amp; approx_a_recip) {</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="keyword">using</span> Scalar = <span class="keyword">typename</span> unpacket_traits&lt;Packet&gt;::type;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    <span class="keyword">const</span> Packet two = pset1&lt;Packet&gt;(Scalar(2));</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="comment">// Refine the approximation using one Newton-Raphson step:</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    <span class="comment">//   x_{i} = x_{i-1} * (2 - a * x_{i-1})</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;     <span class="keyword">const</span> Packet x =</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;         generic_reciprocal_newton_step&lt;Packet,Steps - 1&gt;::run(a, approx_a_recip);</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;     <span class="keyword">const</span> Packet tmp = pnmadd(a, x, two);</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;     <span class="comment">// If tmp is NaN, it means that a is either +/-0 or +/-Inf.</span></div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;     <span class="comment">// In this case return the approximation directly.</span></div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;     <span class="keyword">const</span> Packet is_not_nan = pcmp_eq(tmp, tmp);</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;     <span class="keywordflow">return</span> pselect(is_not_nan, pmul(x, tmp), x);</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;  }</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;};</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160; </div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Packet&gt;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="keyword">struct </span>generic_reciprocal_newton_step&lt;Packet, 0&gt; {</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;   EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE Packet</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;   run(<span class="keyword">const</span> Packet&amp; <span class="comment">/*unused*/</span>, <span class="keyword">const</span> Packet&amp; approx_rsqrt) {</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keywordflow">return</span> approx_rsqrt;</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  }</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;};</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160; </div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Packet, <span class="keywordtype">int</span> Steps&gt;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;<span class="keyword">struct </span>generic_rsqrt_newton_step {</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  static_assert(Steps &gt; 0, <span class="stringliteral">&quot;Steps must be at least 1.&quot;</span>);</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160; </div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE  Packet</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  run(<span class="keyword">const</span> Packet&amp; a, <span class="keyword">const</span> Packet&amp; approx_rsqrt) {</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    <span class="keyword">using</span> Scalar = <span class="keyword">typename</span> unpacket_traits&lt;Packet&gt;::type;</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    <span class="keyword">const</span> Packet one_point_five = pset1&lt;Packet&gt;(Scalar(1.5));</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    <span class="keyword">const</span> Packet minus_half = pset1&lt;Packet&gt;(Scalar(-0.5));</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    </div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <span class="comment">// Refine the approximation using one Newton-Raphson step:</span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <span class="comment">//   x_{n+1} = x_n * (1.5 + (-0.5 * x_n) * (a * x_n)).</span></div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    <span class="comment">// The approximation is expressed this way to avoid over/under-flows.  </span></div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    Packet x_newton  = pmul(approx_rsqrt, pmadd(pmul(minus_half, approx_rsqrt), pmul(a, approx_rsqrt), one_point_five));</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> step = 1; step &lt; Steps; ++step) {</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;      x_newton  = pmul(x_newton, pmadd(pmul(minus_half, x_newton), pmul(a, x_newton), one_point_five));</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    }</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    </div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <span class="comment">// If approx_rsqrt is 0 or +/-inf, we should return it as is.  Note:</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <span class="comment">// on intel, approx_rsqrt can be inf for small denormal values.</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    <span class="keyword">const</span> Packet return_approx = por(pcmp_eq(approx_rsqrt, pzero(a)),</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;                                     pcmp_eq(pabs(approx_rsqrt), pset1&lt;Packet&gt;(NumTraits&lt;Scalar&gt;::infinity())));</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    <span class="keywordflow">return</span> pselect(return_approx, approx_rsqrt, x_newton);</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  }</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;};</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160; </div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Packet&gt;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;<span class="keyword">struct </span>generic_rsqrt_newton_step&lt;Packet, 0&gt; {</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;   EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE Packet</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;   run(<span class="keyword">const</span> Packet&amp; <span class="comment">/*unused*/</span>, <span class="keyword">const</span> Packet&amp; approx_rsqrt) {</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    <span class="keywordflow">return</span> approx_rsqrt;</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  }</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;};</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160; </div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160; </div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Packet, <span class="keywordtype">int</span> Steps=1&gt;</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;<span class="keyword">struct </span>generic_sqrt_newton_step {</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  static_assert(Steps &gt; 0, <span class="stringliteral">&quot;Steps must be at least 1.&quot;</span>);</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160; </div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE  Packet</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  run(<span class="keyword">const</span> Packet&amp; a, <span class="keyword">const</span> Packet&amp; approx_rsqrt) {</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    <span class="keyword">using</span> Scalar = <span class="keyword">typename</span> unpacket_traits&lt;Packet&gt;::type;</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    <span class="keyword">const</span> Packet one_point_five = pset1&lt;Packet&gt;(Scalar(1.5));</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    <span class="keyword">const</span> Packet minus_half = pset1&lt;Packet&gt;(Scalar(-0.5));</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    <span class="comment">// If a is inf or zero, return a directly.</span></div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    <span class="keyword">const</span> Packet inf_mask = pcmp_eq(a, pset1&lt;Packet&gt;(NumTraits&lt;Scalar&gt;::infinity()));</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    <span class="keyword">const</span> Packet return_a = por(pcmp_eq(a, pzero(a)), inf_mask);</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    <span class="comment">// Do a single step of Newton&#39;s iteration for reciprocal square root:</span></div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    <span class="comment">//   x_{n+1} = x_n * (1.5 + (-0.5 * x_n) * (a * x_n))).</span></div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    <span class="comment">// The Newton&#39;s step is computed this way to avoid over/under-flows.</span></div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;    Packet <a class="code" href="namespaceEigen.html#a6374a6a9e972e9358d7ab3fced32d7d5">rsqrt</a> = pmul(approx_rsqrt, pmadd(pmul(minus_half, approx_rsqrt), pmul(a, approx_rsqrt), one_point_five));</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> step = 1; step &lt; Steps; ++step) {</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;      <a class="code" href="namespaceEigen.html#a6374a6a9e972e9358d7ab3fced32d7d5">rsqrt</a> = pmul(<a class="code" href="namespaceEigen.html#a6374a6a9e972e9358d7ab3fced32d7d5">rsqrt</a>, pmadd(pmul(minus_half, <a class="code" href="namespaceEigen.html#a6374a6a9e972e9358d7ab3fced32d7d5">rsqrt</a>), pmul(a, <a class="code" href="namespaceEigen.html#a6374a6a9e972e9358d7ab3fced32d7d5">rsqrt</a>), one_point_five));</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    }</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160; </div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;    <span class="comment">// Return sqrt(x) = x * rsqrt(x) for non-zero finite positive arguments.</span></div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    <span class="comment">// Return a itself for 0 or +inf, NaN for negative arguments.</span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    <span class="keywordflow">return</span> pselect(return_a, a, pmul(a, <a class="code" href="namespaceEigen.html#a6374a6a9e972e9358d7ab3fced32d7d5">rsqrt</a>));</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;  }</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;};</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160; </div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;T generic_fast_tanh_float(<span class="keyword">const</span> T&amp; a_x)</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;{</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  <span class="comment">// Clamp the inputs to the range [-c, c]</span></div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;<span class="preprocessor">#ifdef EIGEN_VECTORIZE_FMA</span></div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;  <span class="keyword">const</span> T plus_clamp = pset1&lt;T&gt;(7.99881172180175781f);</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  <span class="keyword">const</span> T minus_clamp = pset1&lt;T&gt;(-7.99881172180175781f);</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;  <span class="keyword">const</span> T plus_clamp = pset1&lt;T&gt;(7.90531110763549805f);</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;  <span class="keyword">const</span> T minus_clamp = pset1&lt;T&gt;(-7.90531110763549805f);</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;  <span class="keyword">const</span> T tiny = pset1&lt;T&gt;(0.0004f);</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;  <span class="keyword">const</span> T x = pmax(pmin(a_x, plus_clamp), minus_clamp);</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;  <span class="keyword">const</span> T tiny_mask = pcmp_lt(pabs(a_x), tiny);</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;  <span class="comment">// The monomial coefficients of the numerator polynomial (odd).</span></div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;  <span class="keyword">const</span> T alpha_1 = pset1&lt;T&gt;(4.89352455891786e-03f);</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;  <span class="keyword">const</span> T alpha_3 = pset1&lt;T&gt;(6.37261928875436e-04f);</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;  <span class="keyword">const</span> T alpha_5 = pset1&lt;T&gt;(1.48572235717979e-05f);</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;  <span class="keyword">const</span> T alpha_7 = pset1&lt;T&gt;(5.12229709037114e-08f);</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;  <span class="keyword">const</span> T alpha_9 = pset1&lt;T&gt;(-8.60467152213735e-11f);</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;  <span class="keyword">const</span> T alpha_11 = pset1&lt;T&gt;(2.00018790482477e-13f);</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  <span class="keyword">const</span> T alpha_13 = pset1&lt;T&gt;(-2.76076847742355e-16f);</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160; </div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;  <span class="comment">// The monomial coefficients of the denominator polynomial (even).</span></div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;  <span class="keyword">const</span> T beta_0 = pset1&lt;T&gt;(4.89352518554385e-03f);</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;  <span class="keyword">const</span> T beta_2 = pset1&lt;T&gt;(2.26843463243900e-03f);</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;  <span class="keyword">const</span> T beta_4 = pset1&lt;T&gt;(1.18534705686654e-04f);</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;  <span class="keyword">const</span> T beta_6 = pset1&lt;T&gt;(1.19825839466702e-06f);</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160; </div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;  <span class="comment">// Since the polynomials are odd/even, we need x^2.</span></div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;  <span class="keyword">const</span> T x2 = pmul(x, x);</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160; </div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;  <span class="comment">// Evaluate the numerator polynomial p.</span></div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;  T p = pmadd(x2, alpha_13, alpha_11);</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  p = pmadd(x2, p, alpha_9);</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  p = pmadd(x2, p, alpha_7);</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  p = pmadd(x2, p, alpha_5);</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;  p = pmadd(x2, p, alpha_3);</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;  p = pmadd(x2, p, alpha_1);</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;  p = pmul(x, p);</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160; </div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;  <span class="comment">// Evaluate the denominator polynomial q.</span></div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;  T q = pmadd(x2, beta_6, beta_4);</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;  q = pmadd(x2, q, beta_2);</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  q = pmadd(x2, q, beta_0);</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160; </div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;  <span class="comment">// Divide the numerator by the denominator.</span></div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;  <span class="keywordflow">return</span> pselect(tiny_mask, x, pdiv(p, q));</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;}</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160; </div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> RealScalar&gt;</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;RealScalar positive_real_hypot(<span class="keyword">const</span> RealScalar&amp; x, <span class="keyword">const</span> RealScalar&amp; y)</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;{</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;  <span class="comment">// IEEE IEC 6059 special cases.</span></div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;  <span class="keywordflow">if</span> ((numext::isinf)(x) || (numext::isinf)(y))</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    <span class="keywordflow">return</span> NumTraits&lt;RealScalar&gt;::infinity();</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;  <span class="keywordflow">if</span> ((numext::isnan)(x) || (numext::isnan)(y))</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;    <span class="keywordflow">return</span> NumTraits&lt;RealScalar&gt;::quiet_NaN();</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    </div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;  EIGEN_USING_STD(<a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>);</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;  RealScalar p, qp;</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;  p = numext::maxi(x,y);</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;  <span class="keywordflow">if</span>(numext::is_exactly_zero(p)) <span class="keywordflow">return</span> RealScalar(0);</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;  qp = numext::mini(y,x) / p;</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;  <span class="keywordflow">return</span> p * <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(RealScalar(1) + qp*qp);</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;}</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160; </div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;<span class="keyword">struct </span>hypot_impl</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;{</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits&lt;Scalar&gt;::Real RealScalar;</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;  <span class="keyword">static</span> EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;  <span class="keyword">inline</span> RealScalar run(<span class="keyword">const</span> Scalar&amp; x, <span class="keyword">const</span> Scalar&amp; y)</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;  {</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;    EIGEN_USING_STD(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>);</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;    <span class="keywordflow">return</span> positive_real_hypot&lt;RealScalar&gt;(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(x), <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(y));</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;  }</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;};</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160; </div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;<span class="comment">// Generic complex sqrt implementation that correctly handles corner cases</span></div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;<span class="comment">// according to https://en.cppreference.com/w/cpp/numeric/complex/sqrt</span></div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;EIGEN_DEVICE_FUNC std::complex&lt;T&gt; complex_sqrt(<span class="keyword">const</span> std::complex&lt;T&gt;&amp; z) {</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;  <span class="comment">// Computes the principal sqrt of the input.</span></div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;  <span class="comment">//</span></div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;  <span class="comment">// For a complex square root of the number x + i*y. We want to find real</span></div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;  <span class="comment">// numbers u and v such that</span></div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;  <span class="comment">//    (u + i*v)^2 = x + i*y  &lt;=&gt;</span></div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;  <span class="comment">//    u^2 - v^2 + i*2*u*v = x + i*v.</span></div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;  <span class="comment">// By equating the real and imaginary parts we get:</span></div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;  <span class="comment">//    u^2 - v^2 = x</span></div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  <span class="comment">//    2*u*v = y.</span></div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;  <span class="comment">//</span></div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;  <span class="comment">// For x &gt;= 0, this has the numerically stable solution</span></div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;  <span class="comment">//    u = sqrt(0.5 * (x + sqrt(x^2 + y^2)))</span></div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;  <span class="comment">//    v = y / (2 * u)</span></div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;  <span class="comment">// and for x &lt; 0,</span></div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;  <span class="comment">//    v = sign(y) * sqrt(0.5 * (-x + sqrt(x^2 + y^2)))</span></div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;  <span class="comment">//    u = y / (2 * v)</span></div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;  <span class="comment">//</span></div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;  <span class="comment">// Letting w = sqrt(0.5 * (|x| + |z|)),</span></div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;  <span class="comment">//   if x == 0: u = w, v = sign(y) * w</span></div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;  <span class="comment">//   if x &gt; 0:  u = w, v = y / (2 * w)</span></div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;  <span class="comment">//   if x &lt; 0:  u = |y| / (2 * w), v = sign(y) * w</span></div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160; </div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;  <span class="keyword">const</span> T x = numext::real(z);</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;  <span class="keyword">const</span> T y = numext::imag(z);</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;  <span class="keyword">const</span> T zero = T(0);</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;  <span class="keyword">const</span> T w = numext::sqrt(T(0.5) * (numext::abs(x) + numext::hypot(x, y)));</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160; </div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;  <span class="keywordflow">return</span></div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;    (numext::isinf)(y) ? std::complex&lt;T&gt;(NumTraits&lt;T&gt;::infinity(), y)</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;      : numext::is_exactly_zero(x) ? std::complex&lt;T&gt;(w, y &lt; zero ? -w : w)</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;                                   : x &gt; zero ? std::complex&lt;T&gt;(w, y / (2 * w))</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;      : std::complex&lt;T&gt;(numext::<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(y) / (2 * w), y &lt; zero ? -w : w );</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;}</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160; </div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;<span class="comment">// Generic complex rsqrt implementation.</span></div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;EIGEN_DEVICE_FUNC std::complex&lt;T&gt; complex_rsqrt(<span class="keyword">const</span> std::complex&lt;T&gt;&amp; z) {</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;  <span class="comment">// Computes the principal reciprocal sqrt of the input.</span></div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;  <span class="comment">//</span></div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;  <span class="comment">// For a complex reciprocal square root of the number z = x + i*y. We want to</span></div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;  <span class="comment">// find real numbers u and v such that</span></div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;  <span class="comment">//    (u + i*v)^2 = 1 / (x + i*y)  &lt;=&gt;</span></div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;  <span class="comment">//    u^2 - v^2 + i*2*u*v = x/|z|^2 - i*v/|z|^2.</span></div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;  <span class="comment">// By equating the real and imaginary parts we get:</span></div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;  <span class="comment">//    u^2 - v^2 = x/|z|^2</span></div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;  <span class="comment">//    2*u*v = y/|z|^2.</span></div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;  <span class="comment">//</span></div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;  <span class="comment">// For x &gt;= 0, this has the numerically stable solution</span></div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;  <span class="comment">//    u = sqrt(0.5 * (x + |z|)) / |z|</span></div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;  <span class="comment">//    v = -y / (2 * u * |z|)</span></div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;  <span class="comment">// and for x &lt; 0,</span></div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  <span class="comment">//    v = -sign(y) * sqrt(0.5 * (-x + |z|)) / |z|</span></div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;  <span class="comment">//    u = -y / (2 * v * |z|)</span></div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;  <span class="comment">//</span></div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;  <span class="comment">// Letting w = sqrt(0.5 * (|x| + |z|)),</span></div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;  <span class="comment">//   if x == 0: u = w / |z|, v = -sign(y) * w / |z|</span></div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;  <span class="comment">//   if x &gt; 0:  u = w / |z|, v = -y / (2 * w * |z|)</span></div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;  <span class="comment">//   if x &lt; 0:  u = |y| / (2 * w * |z|), v = -sign(y) * w / |z|</span></div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160; </div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;  <span class="keyword">const</span> T x = numext::real(z);</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;  <span class="keyword">const</span> T y = numext::imag(z);</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;  <span class="keyword">const</span> T zero = T(0);</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160; </div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;  <span class="keyword">const</span> T abs_z = numext::hypot(x, y);</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;  <span class="keyword">const</span> T w = numext::sqrt(T(0.5) * (numext::abs(x) + abs_z));</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;  <span class="keyword">const</span> T woz = w / abs_z;</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;  <span class="comment">// Corner cases consistent with 1/sqrt(z) on gcc/clang.</span></div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;  <span class="keywordflow">return</span></div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;          numext::is_exactly_zero(abs_z) ? std::complex&lt;T&gt;(NumTraits&lt;T&gt;::infinity(), NumTraits&lt;T&gt;::quiet_NaN())</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;                                         : ((numext::<a class="code" href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">isinf</a>)(x) || (numext::<a class="code" href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">isinf</a>)(y)) ? std::complex&lt;T&gt;(zero, zero)</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;      : numext::is_exactly_zero(x) ? std::complex&lt;T&gt;(woz, y &lt; zero ? woz : -woz)</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;                                   : x &gt; zero ? std::complex&lt;T&gt;(woz, -y / (2 * w * abs_z))</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;      : std::complex&lt;T&gt;(numext::<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(y) / (2 * w * abs_z), y &lt; zero ? woz : -woz );</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;}</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160; </div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;EIGEN_DEVICE_FUNC std::complex&lt;T&gt; complex_log(<span class="keyword">const</span> std::complex&lt;T&gt;&amp; z) {</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;  <span class="comment">// Computes complex log.</span></div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;  T a = numext::abs(z);</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;  EIGEN_USING_STD(atan2);</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;  T b = atan2(z.imag(), z.real());</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;  <span class="keywordflow">return</span> std::complex&lt;T&gt;(numext::log(a), b);</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;}</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160; </div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160; </div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160; </div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_MATHFUNCTIONSIMPL_H</span></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a1f1103712e337c4c96a05f949637a4c8"><div class="ttname"><a href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">Eigen::isinf</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_isinf_op&lt; typename Derived::Scalar &gt;, const Derived &gt; isinf(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a6374a6a9e972e9358d7ab3fced32d7d5"><div class="ttname"><a href="namespaceEigen.html#a6374a6a9e972e9358d7ab3fced32d7d5">Eigen::rsqrt</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_rsqrt_op&lt; typename Derived::Scalar &gt;, const Derived &gt; rsqrt(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_af4f536e8ea56702e63088efb3706d1f0"><div class="ttname"><a href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">Eigen::sqrt</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sqrt_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sqrt(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
  <ul>
    <li class="navelem"><a class="el" href="dir_a62d91f57b5fefafb116d3f5c1ce792a.html">Eigen</a></li><li class="navelem"><a class="el" href="dir_f84311377820247c2dbcf5d6a63ab308.html">src</a></li><li class="navelem"><a class="el" href="dir_c5b8aa1b6d8d74c5127fb52cc05e6083.html">Core</a></li><li class="navelem"><b>MathFunctionsImpl.h</b></li>
    <li class="footer">Generated on Thu Apr 21 2022 13:07:51 for Eigen by
    <a href="http://www.doxygen.org/index.html">
    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.9.1 </li>
  </ul>
</div>
</body>
</html>
